# You have 7,232 grams of a radioactive kind of uranium. How much will be left after 56 hours if its half-life is 14 hours?

May 27, 2017

$452 \text{g U}$

#### Explanation:

We're asked to find how much uranium remains after a given time ($56 \text{hr}$), when given its initial amount ($7232 \text{g}$) and its half-life ($14 \text{hr}$).

When solving half-life problems like this one, we can use the equation

m(t) = m_0(1/2)^((t)/(t_(1/2)

where
$m \left(t\right)$ is the mass of the remaining mass of the decaying substance,
${m}_{0}$ is the initial mass of the substance,
$t$ is the time (in whatever the unit the half-life is, in this case hours), and
${t}_{\frac{1}{2}}$ is the half-life of the substance.

(In case it's difficult to see, the exponent on the $\frac{1}{2}$ is $\frac{t}{{t}_{\frac{1}{2}}}$)

Plugging in known variables, the equation becomes

m(t) = (7232"g")(1/2)^((56cancel("hr"))/(14 cancel("hr"))

= color(red)(452 "g U"